Electronic Journal of Differential Equations, 2014 Summary: By using the genus properties, we establish some criteria for the second-order \(p(t)\)-Laplacian system \[ {d\over dt} (|\dot u(t)|^{p(t)-2}\dot u(t))- a(t)|u(t)|^{p(t)-2} u(t)+\nabla W(t,u(t))= 0 \] to have at least one, and infinitely many homoclinic orbits, where \(t\in\mathbb{R}\), \(u\in\mathbb{R}^N\), \(p(t)\in C(\mathbb{R},\mathbb{R})\)
Bin Qin, Peng Chen
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Mixed-mode oscillations with multiple time scales [PDF]
, 2010 Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes.
Desroches, MF +5 more
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On a Two Dimensional Reaction-Diffusion System with Hypercyclical Structure [PDF]
, 2000 We study a hypercyclical reaction-diffusion system which arises in the modeling of catalytic networks and describes the emerging of cluster states.
Winter, M, Wei, J
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Multiple Fast Homoclinic Solutions for a Class of Second-Order Differential Systems with p-Laplacian
Ukrainian Mathematical JournalUDC 517.9 We study the existence of multiple fast homoclinic solutions for a class of second-order differential systems with $p$-Laplacian by using the minimax methods in the critical-point theory.
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Homoclinic and quasi-homoclinic solutions for damped differential equations
, 2015 We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t,u)=0, $$ where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on
Chuan-Fang Zhang, Zhi-Qing Han
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Open Journal of Mathematical Analysis<p>This article concerns the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation with <span class="math inline">\(p-\)</span>Laplacian <span class="math display">\[\Big(\left|u''(t)\right|^{p-2}u''(t)\Big)''-\omega\Big(\left|u&
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Sequential buckling in fluid-filled cylindrical shells. [PDF]
Commun PhysJain S +4 more
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Revealing homoclinic breather waves, periodic lump waves and other waves forms of an integrable reduced spin Hirota-Maxwell-Bloch system. [PDF]
Sci RepCeesay B +4 more
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On a Countable Sequence of Homoclinic Orbits Arising Near a Saddle-Center Point. [PDF]
Commun Math PhysBaldomá I, Guardia M, Pelinovsky DE.
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Dynamical analysis of lump, breather, M-shaped and other wave profiles propagating in a nonlinear PDE describing the nonlinear low-pass electrical transmission lines. [PDF]
Sci RepBaber MZ, Shafee A, Ceesay B, Ahmed N.
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